diffalg(deprecated)/greater - Help

diffalg

 greater
 compare the rank of two differential polynomials

 Calling Sequence greater (p, q, R)

Parameters

 p, q - differential polynomials in R R - differential polynomial ring

Description

 • Important: The diffalg package has been deprecated. Use the superseding package DifferentialAlgebra instead.
 • The function greater returns true if the rank of p is greater than the one of q. Otherwise, false is returned.
 • p has greater rank than q if
 (a)  q belongs to the ground field of R and p does not,
 (b)  the leader of p is greater than the leader of q with respect to the ranking of R, or
 (c)  p and q have the same leader  and the degree,  in  this common leader,  of  p is greater than the one of  q.
 • The function greater provides only a pre-order on R.
 • The command with(diffalg,greater) allows the use of the abbreviated form of this command.

Examples

Important: The diffalg package has been deprecated. Use the superseding package DifferentialAlgebra instead.

 > $\mathrm{with}\left(\mathrm{diffalg}\right):$
 > $R≔\mathrm{differential_ring}\left(\mathrm{derivations}=\left[x,y\right],\mathrm{ranking}=\left[{\mathrm{lex}}_{u}\right]\right)$
 ${R}{:=}{\mathrm{PDE_ring}}$ (1)
 > $\mathrm{greater}\left({u}_{x},{u}_{y,y},R\right)$
 ${\mathrm{true}}$ (2)
 > $\mathrm{greater}\left({u}_{x,x}^{2}+{u}_{y},{u}_{y,y}^{5}{u}_{x,x}^{2}+1,R\right)$
 ${\mathrm{false}}$ (3)